I just wanted to inform that, while we wait for a true update of Stadia to be playable on our IOS devices, we still have a workaround for now which is the Google remote desktop app.
1) first you must download the Google remote desktop app in the app store. The app will guide you in the next steps.
2) You need to go to the following link in chrome : https://remotedesktop.google.com/access/
3) you will need to download the chrome extension in the page you just opened
4) you will setup a digit code and find your computer
5) then you will have to refresh the page
Once all is done, you can actually launch Stadia in chrome from your computer browser, and play on your ios device in the app! Keep in mind this is very limited since you need your computer to be around. Other than that, I was able to play some games with a decent quality, with the stadia controller connected to the computer. The input lag is a little more present, so I would suggest to not play a game which requires a lot of precision. The Tomb raider games seem like a good candidate for your trial. I am aware that is only a limited workaround but hey, that gives us a preliminary feeling of playing Stadia on our devices.